分散式儲存編碼(distributed storage coding)被廣泛運用在無線感測網路(WSNs)上。目的在於即便有些感測器(Sensors)因為電池耗盡或外力損害等因素而失效，可以透過編碼的方式還原其感測器的資料。這類相關研究中，如何有效率且具規模地將資料散佈於無線感測網路上是一個挑戰。我們假設N storage sensors 當中有K sensors可以感測資料並以隨機漫步(Random walk)的方式將資料散佈於網路上，每一個感測器隨機選擇一些接收到的資料將其編碼成一筆資料並儲存。本篇論文交叉使用兩種噴泉碼(Fountain Codes)：Luby Transform (LT) codes和Repairable Fountain (RF) codes來處理感測器量測之序列資料(Time series)。在無線感測網路上執行噴泉碼需要長距離(Lengthy hop-count)擴散達到高度隨機性，以提升解碼率(Source decoded rate)。為了有效降低傳輸成本，本論文提出利用時序資料相依度高的特性，不須每筆資料都需要成功解碼，反而利用補償機制來補足解碼失敗資料。我們提出一種架構(Framework)達到上述效果：首先將時序資料分為兩類，t時序倍數採用高解碼率處理(完全還原)；其餘(t-1)時序資料採用較低解碼率處理(部分還原)，最後利用內插估算未被還原的資料。本架構使用LT codes和RF codes提升資料取得的可靠度，以理論估計最適解碼率來大幅降低傳輸量，同時將時序資料還原誤差值(NRMSE)控制在4%以下。

Distributed storage coding has been widely applied on data gathering over unreliable wireless sensor networks (WSNs), where it is essential to ensure the data persistence in case of massive sensor failures caused by battery run-out or some physical damage problems surroundings. How to efficiently and scalably disseminate and collect the sensing data over WSNs is a key challenge yet. In this study, assumed that there are K sensor nodes equipped sensing apparatus within N storage sensors, these K numbers of sensors can sense environmental changes and disseminate coded (by Fountain codes) time-series data over WSNs using the simple random walk. That is, each sensor will receive others’ data, randomly select d (which according to the chosen degree distribution) of them, and encode into an encoded data then store it. In this thesis, we employ two types of Fountain codes: Luby Transform (LT) codes and Repairable Fountain (RF) codes to maintain the level of data persistence. In order to perform the Fountain codes over WSNs, the question is to disseminate data in the long range of random walks to preserve the randomness so as to boost the source decoded rate. In other words, the hop count would be long enough such that the decoding process can be perfectly completed using less amount of redundancy (say 10%).

In this thesis, a framework of less communication cost is proposed due to the temporal dependency of time-series data. The concept is simple: the complete decoding is not necessary for most of time-series data since the missing portions can be compensated by neighbors if exists. Our framework works as follows. We separate time-series data into two categories. For a given number t, the data corresponding to the numbers divisible by t will be totally recovered with high probability; however, the data corresponding to the other time slots is set as partially recovered. As mentioned, the missing one can be interpolated by the nearby neighboring data through temporal dependency. The proposed framework employs LT codes and RF codes to increase the level reliability. Besides, a mathematical model to estimate the appropriate source decoded rate is proposed to reduce the transmission cost (hop count) while maintaining tolerable level (< 4% normalized root-mean-square error (NRMSE)) of errors as well.

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